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Binary field arithmetic contributed by Sun Microsystems.

The 'OPENSSL_NO_SUN_DIV' default is still subject to change,
so I didn't bother to finish the CHANGES entry yet.

Submitted by: Douglas Stebila <>, Sheueling Chang <>
(CHANGES entry by Bodo Moeller)
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45264 committed Aug 2, 2002
1 parent 16dc1cf commit 1dc920c8de5b7109727a21163843feecdf06a8cf
Showing with 1,768 additions and 3 deletions.
  1. +52 −0 CHANGES
  2. +9 −2 crypto/bn/Makefile.ssl
  3. +68 −0 crypto/bn/bn.h
  4. +9 −1 crypto/bn/bn_err.c
  5. +984 −0 crypto/bn/bn_gf2m.c
  6. +646 −0 crypto/bn/bntest.c
@@ -4,6 +4,58 @@

Changes between 0.9.7 and 0.9.8 [xx XXX 2002]

*) Add binary polynomial arithmetic software in crypto/bn/bn_gf2m.c.
Polynomials are represented as BIGNUMs (where the sign bit is not
used) in the following functions [macros]:

BN_GF2m_sub [= BN_GF2m_add]
BN_GF2m_mod [wrapper for BN_GF2m_mod_arr]
BN_GF2m_mod_mul [wrapper for BN_GF2m_mod_mul_arr]
BN_GF2m_mod_sqr [wrapper for BN_GF2m_mod_sqr_arr]
BN_GF2m_mod_exp [wrapper for BN_GF2m_mod_exp_arr]
BN_GF2m_mod_sqrt [wrapper for BN_GF2m_mod_sqrt_arr]
BN_GF2m_mod_solve_quad [wrapper for BN_GF2m_mod_solve_quad_arr]
BN_GF2m_cmp [= BN_ucmp]

(Note that only the 'mod' functions are actually for fields GF(2^m).
BN_GF2m_add() is misnomer, but this is for the sake of consistency.)

For some functions, an the irreducible polynomial defining a
field can be given as an 'unsigned int[]' with strictly
decreasing elements giving the indices of those bits that are set;
i.e., p[] represents the polynomial
f(t) = t^p[0] + t^p[1] + ... + t^p[k]
p[0] > p[1] > ... > p[k] = 0.
This applies to the following functions:

BN_GF2m_mod_inv_arr [wrapper for BN_GF2m_mod_inv]
BN_GF2m_mod_div_arr [wrapper for BN_GF2m_mod_div]

Conversion can be performed by the following functions:


bntest.c has additional tests for binary polynomial arithmetic.

Two implementations for BN_GF2m_mod_div() are available (selected
at compile-time). ...

[Sheueling Chang Shantz and Douglas Stebila
(Sun Microsystems Laboratories)]

*) Add more WAP/WTLS elliptic curve OIDs.
[Douglas Stebila <>]

@@ -39,12 +39,12 @@ LIB=$(TOP)/libcrypto.a
LIBSRC= bn_add.c bn_div.c bn_exp.c bn_lib.c bn_ctx.c bn_mul.c bn_mod.c \
bn_print.c bn_rand.c bn_shift.c bn_word.c bn_blind.c \
bn_kron.c bn_sqrt.c bn_gcd.c bn_prime.c bn_err.c bn_sqr.c bn_asm.c \
bn_recp.c bn_mont.c bn_mpi.c bn_exp2.c
bn_recp.c bn_mont.c bn_mpi.c bn_exp2.c bn_gf2m.c

LIBOBJ= bn_add.o bn_div.o bn_exp.o bn_lib.o bn_ctx.o bn_mul.o bn_mod.o \
bn_print.o bn_rand.o bn_shift.o bn_word.o bn_blind.o \
bn_kron.o bn_sqrt.o bn_gcd.o bn_prime.o bn_err.o bn_sqr.o $(BN_ASM) \
bn_recp.o bn_mont.o bn_mpi.o bn_exp2.o
bn_recp.o bn_mont.o bn_mpi.o bn_exp2.o bn_gf2m.o


@@ -194,6 +194,13 @@ bn_asm.o: ../../include/openssl/lhash.h ../../include/openssl/opensslconf.h
bn_asm.o: ../../include/openssl/opensslv.h ../../include/openssl/safestack.h
bn_asm.o: ../../include/openssl/stack.h ../../include/openssl/symhacks.h
bn_asm.o: ../cryptlib.h bn_asm.c bn_lcl.h
bn_gf2m.o: ../../e_os.h ../../include/openssl/bio.h ../../include/openssl/bn.h
bn_gf2m.o: ../../include/openssl/buffer.h ../../include/openssl/crypto.h
bn_gf2m.o: ../../include/openssl/e_os2.h ../../include/openssl/err.h
bn_gf2m.o: ../../include/openssl/lhash.h ../../include/openssl/opensslconf.h
bn_gf2m.o: ../../include/openssl/opensslv.h ../../include/openssl/safestack.h
bn_gf2m.o: ../../include/openssl/stack.h ../../include/openssl/symhacks.h
bn_gf2m.o: ../cryptlib.h bn_gf2m.c bn_lcl.h
bn_blind.o: ../../e_os.h ../../include/openssl/bio.h ../../include/openssl/bn.h
bn_blind.o: ../../include/openssl/buffer.h ../../include/openssl/crypto.h
bn_blind.o: ../../include/openssl/e_os2.h ../../include/openssl/err.h
@@ -55,6 +55,32 @@
* copied and put under another distribution licence
* [including the GNU Public Licence.]
/* ====================================================================
* Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
* Portions of the attached software ("Contribution") are developed by
* SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
* The Contribution is licensed pursuant to the Eric Young open source
* license provided above.
* In addition, Sun covenants to all licensees who provide a reciprocal
* covenant with respect to their own patents if any, not to sue under
* current and future patent claims necessarily infringed by the making,
* using, practicing, selling, offering for sale and/or otherwise
* disposing of the Contribution as delivered hereunder
* (or portions thereof), provided that such covenant shall not apply:
* 1) for code that a licensee deletes from the Contribution;
* 2) separates from the Contribution; or
* 3) for infringements caused by:
* i) the modification of the Contribution or
* ii) the combination of the Contribution with other software or
* devices where such combination causes the infringement.
* The binary polynomial arithmetic software is originally written by
* Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.

#ifndef HEADER_BN_H
#define HEADER_BN_H
@@ -453,6 +479,40 @@ int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m,
BN_RECP_CTX *recp, BN_CTX *ctx);

/* Functions for arithmetic over binary polynomials represented by BIGNUMs.
* The BIGNUM::neg property of BIGNUMs representing binary polynomials is ignored.
* Note that input arguments are not const so that their bit arrays can
* be expanded to the appropriate size if needed.
int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); /* r = a + b */
#define BN_GF2m_sub(r, a, b) BN_GF2m_add(r, a, b)
int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p); /* r = a mod p */
int BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx); /* r = (a * b) mod p */
int BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx); /* r = (a * a) mod p */
int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx); /* r = (1 / b) mod p */
int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx); /* r = (a / b) mod p */
int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx); /* r = (a ^ b) mod p */
int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx); /* r = sqrt(a) mod p */
int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx); /* r^2 + r = a mod p */
#define BN_GF2m_cmp(a, b) BN_ucmp((a), (b))
/* Some functions allow for representation of the irreducible polynomials
* as an unsigned int[], say p. The irreducible f(t) is then of the form:
* t^p[0] + t^p[1] + ... + t^p[k]
* where m = p[0] > p[1] > ... > p[k] = 0.
int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[]); /* r = a mod p */
int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const unsigned int p[], BN_CTX *ctx); /* r = (a * b) mod p */
int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[], BN_CTX *ctx); /* r = (a * a) mod p */
int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *b, const unsigned int p[], BN_CTX *ctx); /* r = (1 / b) mod p */
int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const unsigned int p[], BN_CTX *ctx); /* r = (a / b) mod p */
int BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const unsigned int p[], BN_CTX *ctx); /* r = (a ^ b) mod p */
int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[], BN_CTX *ctx); /* r = sqrt(a) mod p */
int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[], BN_CTX *ctx); /* r^2 + r = a mod p */
int BN_GF2m_poly2arr(const BIGNUM *a, unsigned int p[], int max);
int BN_GF2m_arr2poly(const unsigned int p[], BIGNUM *a);

/* library internal functions */

#define bn_expand(a,bits) ((((((bits+BN_BITS2-1))/BN_BITS2)) <= (a)->dmax)?\
@@ -510,6 +570,13 @@ void ERR_load_BN_strings(void);
#define BN_F_BN_DIV 107
#define BN_F_BN_EXPAND2 108
#define BN_F_BN_GF2M_MOD 126
#define BN_F_BN_GF2M_MOD_DIV 123
#define BN_F_BN_GF2M_MOD_EXP 127
#define BN_F_BN_GF2M_MOD_MUL 124
#define BN_F_BN_GF2M_MOD_SQR 125
#define BN_F_BN_MOD_EXP2_MONT 118
#define BN_F_BN_MOD_EXP_MONT 109
@@ -535,6 +602,7 @@ void ERR_load_BN_strings(void);
#define BN_R_INVALID_RANGE 115
#define BN_R_NOT_A_SQUARE 111
#define BN_R_NO_INVERSE 108
#define BN_R_P_IS_NOT_PRIME 112
@@ -1,6 +1,6 @@
/* crypto/bn/bn_err.c */
/* ====================================================================
* Copyright (c) 1999 The OpenSSL Project. All rights reserved.
* Copyright (c) 1999-2002 The OpenSSL Project. All rights reserved.
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
@@ -77,6 +77,13 @@ static ERR_STRING_DATA BN_str_functs[]=
{ERR_PACK(0,BN_F_BN_DIV,0), "BN_div"},
{ERR_PACK(0,BN_F_BN_EXPAND2,0), "bn_expand2"},
{ERR_PACK(0,BN_F_BN_GF2M_MOD,0), "BN_GF2m_mod"},
{ERR_PACK(0,BN_F_BN_GF2M_MOD_DIV,0), "BN_GF2m_mod_div"},
{ERR_PACK(0,BN_F_BN_GF2M_MOD_EXP,0), "BN_GF2m_mod_exp"},
{ERR_PACK(0,BN_F_BN_GF2M_MOD_MUL,0), "BN_GF2m_mod_mul"},
{ERR_PACK(0,BN_F_BN_GF2M_MOD_SOLVE_QUAD,0), "BN_GF2m_mod_solve_quad"},
{ERR_PACK(0,BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR,0), "BN_GF2m_mod_solve_quad_arr"},
{ERR_PACK(0,BN_F_BN_GF2M_MOD_SQR,0), "BN_GF2m_mod_sqr"},
{ERR_PACK(0,BN_F_BN_MOD_EXP2_MONT,0), "BN_mod_exp2_mont"},
{ERR_PACK(0,BN_F_BN_MOD_EXP_MONT,0), "BN_mod_exp_mont"},
{ERR_PACK(0,BN_F_BN_MOD_EXP_MONT_WORD,0), "BN_mod_exp_mont_word"},
@@ -105,6 +112,7 @@ static ERR_STRING_DATA BN_str_reasons[]=
{BN_R_INVALID_LENGTH ,"invalid length"},
{BN_R_INVALID_RANGE ,"invalid range"},
{BN_R_NOT_A_SQUARE ,"not a square"},
{BN_R_NOT_IMPLEMENTED ,"not implemented"},
{BN_R_NOT_INITIALIZED ,"not initialized"},
{BN_R_NO_INVERSE ,"no inverse"},
{BN_R_P_IS_NOT_PRIME ,"p is not prime"},
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